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# Isoelectric Point Calculation

By rearranging the Henderson-Hasselbalch equation:

$\text{pH}=\text{pK}_\text{a} + \log\left(\dfrac{\text{[A}^{-}\text{]}}{\text{[HA]}}\right)$

we can get the ratio between an acid and its conjugate base:

$\frac{\text{[HA]}}{\text{[A}^{-}\text{]}}=10^{(\text{pK}_\text{a}-\text{pH})}$

and between an base and its conjugate acid:

$\frac{\text{[B]}}{\text{[BH}^+\text{]}} = 10^{(\text{pH}-\text{pK}_\text{a})}$

Thus, the proportion of deprotonated acid is calculated as follows:

$\dfrac{\text{[A}^{-}\text{]}}{\text{[A]}_\text{total}}=\dfrac{\text{[A}^{-}\text{]}}{\text{[HA]}+\text{[A}^{-}\text{]}}=\dfrac{1}{1+\frac{\text{[HA]}}{\text{[A}^{-}\text{]}}}=\dfrac{1}{1+10^{(\text{pK}_\text{a}-\text{pH})}}$

Similarly, for basic species:

$\dfrac{\text{[BH}^+\text{]}}{\text{[B]}_\text{total}}=\dfrac{\text{[BH}^+\text{]}}{\text{[B]}+\text{[BH}^+\text{]}}=\dfrac{1}{1+\frac{\text{[B]}}{\text{[BH}^+\text{]}}}=\dfrac{1}{1+10^{(\text{pH}-\text{pK}_\text{a})}}$

http://fields.scripps.edu/DTASelect/20010710-pI-Algorithm.pdf